ellipse_bounds

safe_learning.utilities.ellipse_bounds(P, level, n=100)

Compute the bounds of a 2D ellipse.

The levelset of the ellipsoid is given by level = x’ P x. Given the coordinates of the first dimension, this function computes the corresponding lower and upper values of the second dimension and removes any values of x0 that are outside of the ellipse.

Parameters:

P : np.array

The matrix of the ellipsoid

level : float

The value of the levelset

n : int

Number of data points

Returns:

x : np.array

1D array of x positions of the ellipse

yu : np.array

The upper bound of the ellipse

yl : np.array

The lower bound of the ellipse

Notes

This can be used as `plt.fill_between(*ellipse_bounds(P, level))`